A major goal of research in Clinical Pharmacology is to characterize and understand the quantitative relationships between drug exposure and drug effects. While research questions largely justify development of the methodology we study, there is also a more practical motivation: to optimally individualize the use of effective but toxic drugs requires considerable knowledge of the relationship between drug exposure, response(s) and patient characteristics, the so-called response surface. Model-based analysis of PK/PD data arising from many sources is increasingly seen as a means to knowledge of the response surface, and thence to better dosage and better clinical outcomes. Satisfactory mechanistic models to describe PK/PD are often difficult to devise a priori; exploratory analyses using flexible (non-parametric) models allow "the data to speak", and to suggest subsequent mechanistic models. Ideally this exploratory/mechanistic model spectrum is not a dichotomy: at any stage one uses models that make assumptions no stronger than one wishes. We call models that incorporate certain assumptions, yet are non-committal about others, semi-parametric. The advent of computation-intensive methods for modeling and estimation that avoid the need for mathematical tractability, combined with the increasing availability of more sophisticated and precise PD measurements sets the stage for major advances in semi-parametric PK/PD modeling. Our specific aims are therefore to: I. Devise semiparametric models for PK/PD data analysis. For linear systems (mostly PK), we will seek to improve deconvolution methods. For PD we will focus on models for the interaction of multiple inputs (drugs and other effects, such as other drugs), and non-standard data: (i) dichotomous, (ii) categorical, and (iii) ordered categorical. We will also devise models/methods for multivariate responses, paying particular attention to the problem of dimensional reduction. 2. Adapt our models for analysis of population PK/PD data. To this end, we will pay particular attention to the interface with the computer program NON-MEM; and 3. Apply our models/methods to real- world data. If the models/methods we develop are to continue to have significant impact on drug development, regulation, and evaluation, it is essential that they be tested and refined in real-world drug studies.